October 29
3:00pm, BRH 109
Matthew Krauel
(Sacramento State)

Title:
In Search of New Algebraic Structures, Part I

Abstract:
Loosely speaking, representation theory is the study of algebraic structures by representing their elements as matrices and its product as the product of matrices. This essentially reduces many problems to linear algebra. It is an overarching goal in mathematical theories to classify representations for a given algebraic structure. Often, knowledge of a substructure can be used in this process, and in particular to create new representations by utilizing representations of the substructure. However, in some areas of mathematics and physics, such as 2dimensional conformal field theory, this process is opaque.
In this talk, I will introduce the concepts of representations in the theory of groups and describe some of the fundamental machinery in this area. I will then proceed to explain how this theory also works (or doesn't) with other algebraic structures. The goal will be to build towards explaining an open problem that persists among a number of important algebraic structures, and in particular Lie algebras, where an answer would have ramifications in conformal field theory.